Problem: Simplify to lowest terms. $\dfrac{20}{24}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 20 and 24? $20 = 2\cdot2\cdot5$ $24 = 2\cdot2\cdot2\cdot3$ $\mbox{GCD}(20, 24) = 2\cdot2 = 4$ $\dfrac{20}{24} = \dfrac{5 \cdot 4}{ 6\cdot 4}$ $\hphantom{\dfrac{20}{24}} = \dfrac{5}{6} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{20}{24}} = \dfrac{5}{6} \cdot 1$ $\hphantom{\dfrac{20}{24}} = \dfrac{5}{6}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{20}{24}= \dfrac{2\cdot10}{2\cdot12}= \dfrac{2\cdot 2\cdot5}{2\cdot 2\cdot6}= \dfrac{5}{6}$